An extrusion process is one of the most economic methods of manufacturing to produce engineering structural materials. Typically, an extrusion process is used to manufacture lengths of extruded members having a uniform cross-section. The cross-section of the members may be of various simple shapes such as circular, annular, or rectangular. The cross-section of the members may also be very complex, including internal support structures and/or having an irregular periphery.
Typically, an extrusion process utilizes thermoplastic polymer compounds that are introduced into a feed hopper, Thermoplastic polymer compounds can be in powder, liquid, cubed, palletized and/or any other extrudable form. The thermoplastic polymer can be virgin, recycled, or a mixture of both. An example of a typical extruder is shown in FIG. 1.
The plastic industry has used fillers to lower resin costs during manufacturing. Typical fillers include calcium carbonate, talc, wood fiber, and a variety of others. In addition to providing a cost savings, adding fillers to plastics reduces the coefficient of thermal expansion, increases mechanical strength, and in some cases lowers the density.
Calcium carbonate and talc have no structural strength or fiber orientation to improve structural stability. Talc is bonded together by weak Van der Waal's forces, which allow the material to cleave again and again when pressure is applied to its surface. Even though test results indicate that talc imparts a variety of benefits to polymers, for instance higher stiffness and improved dimensional stability, talc acts like a micro-filler with lubricating properties.
Calcium carbonate has similar properties, but has a water absorption problem, which limits its application because of environmental degradation. Talc avoids this problem since it is hydrophobic.
Wood fiber adds some dimensional stability because of the fiber characteristics interaction with the plastic but wood fiber also suffers from environmental degradation. All three of these common fillers are economically feasible but are structurally limited.
Research efforts have focused on farm waste fibers such as rice hulls, sugar cane fiber, wheat straw and a variety of other fibers to be used as low-cost fillers inside plastics. The use of wood fiber as a filler presents similar difficulties to the above-referenced farm waste fibers.
There are three types of commonly used mixing principles:
1. Static mixing: liquids flowing around fixed objects either by force produced flow by pressure through mechanical means or gravity induced flow.
2. Dynamic mixing: liquid induced mixing by mechanical agitation with typical impellers, i.e., impellers and wiping blade and sheer designs as well as dual or single screw agitation designs.
3. Kinetic mixing: liquid is mixed by velocity impacts on a surface or impacts of two or more liquids impinging on each other.
All three of the above mixing methods have one thing in common that hinders the optimizing of mixing regardless of the fluid being combined and regardless of whether the materials being mixed are polar, nonpolar, organic or inorganic etc. or if it is a filled material with compressible or non-compressible fillers.
All incompressible fluids have a wall effect or a boundary layer effect where the fluid velocity is greatly reduced at the wall or mechanical interface. Static mixing systems use this boundary layer to fold or blend the liquid using this resistive force to promote agitation.
Dynamic mixing, regardless of the geometry of mixing blades or turbine, results in dead zones and incomplete mixing because of the boundary layer. Dynamic mixing uses high shear and a screw blade designed to use the boundary layer to promote friction and compression by centrifugal forces to accomplish agitation while maintaining an incomplete mixed boundary layer on mechanical surfaces.
Kinetic mixing suffers from boundary layer effects on velocity profiles both on the incoming streams and at the injector tip. However, this system suffers minimal effects of boundary layer except for transport fluid phenomena.
A further explanation of the boundary layer follows. Aerodynamic forces depend in a complex way on the viscosity of the fluid. As the fluid moves past the object, the molecules right next to the surface stick to the surface. The molecules just above the surface are slowed down in their collisions with the molecules sticking to the surface. These molecules in turn slow down the flow just above them. The farther one moves away from the surface, the fewer the collisions affected by the object surface. This creates a thin layer of fluid near the surface in which the velocity changes from zero at the surface to the free stream value away from the surface. Engineers call this layer the boundary layer because it occurs on the boundary of the fluid.
As an object moves through a fluid, or as a fluid moves past an object, the molecules of the fluid near the object are disturbed and move around the object. Aerodynamic forces are generated between the fluid and the object. The magnitude of these forces depend on the shape of the object, the speed of the object, the mass of the fluid going by the object and on two other important properties of the fluid; the viscosity, or stickiness, and the compressibility, or springiness, of the fluid. To properly model these effects, aerospace engineers use similarity parameters which are ratios of these effects to other forces present in the problem. If two experiments have the same values for the similarity parameters, then the relative importance of the forces are being correctly modeled.
FIG. 2A shows the streamwise velocity variation from free stream to the surface. In reality, the effects are three dimensional. From the conservation of mass in three dimensions, a change in velocity in the streamwise direction causes a change in velocity in the other directions as well. There is a small component of velocity perpendicular to the surface which displaces or moves the flow above it. One can define the thickness of the boundary layer to be the amount of this displacement. The displacement thickness depends on the Reynolds number, which is the ratio of inertial (resistant to change or motion) forces to viscous (heavy and gluey) forces and is given by the equation: Reynolds number (Re) equals velocity (V) times density (r) times a characteristic length (l) divided by the viscosity coefficient (mu), i.e., Re=V*r*l/mu.
As can be seen in FIG. 2A, boundary layers may be either laminar (layered), or turbulent (disordered) depending on the value of the Reynolds number. For lower Reynolds numbers, the boundary layer is laminar and the streamwise velocity changes uniformly as one moves away from the wall, as shown on the left side of FIG. 2A. For higher Reynolds numbers, the boundary layer is turbulent and the streamwise velocity is characterized by unsteady (changing with time) swirling flows inside the boundary layer. The external flow reacts to the edge of the boundary layer just as it would to the physical surface of an object. So the boundary layer gives any object an “effective” shape which is usually slightly different from the physical shape. The boundary layer may lift off or “separate” from the body and create an effective shape much different from the physical shape. This happens because the flow in the boundary has very low energy (relative to the free stream) and is more easily driven by changes in pressure. Flow separation is the reason for airplane wing stall at high angle of attack. The effects of the boundary layer on lift are contained in the lift coefficient and the effects on drag are contained in the drag coefficient.
Boundary-Layer Flow
That portion of a fluid flow, near a solid surface, is where shear stresses are significant and inviscid-flow assumption may not be used. All solid surfaces interact with a viscous fluid flow because of the no-slip condition, a physical requirement that the fluid and solid have equal velocities at their interface. Thus, a fluid flow is retarded by a fixed solid surface, and a finite, slow-moving boundary layer is formed. A requirement for the boundary layer to be thin is that the Reynolds number of the body be large, 103 or more. Under these conditions the flow outside the boundary layer is essentially inviscid and plays the role of a driving mechanism for the layer.
Referring now to FIG. 2B, a typical low-speed or laminar boundary layer is shown in the illustration. Such a display of the streamwise flow vector variation near the wall is called a velocity profile. The no-slip condition requires that u(x,0)=0, as shown, where u is the velocity of flow in the boundary layer. The velocity rises monotonically with distance y from the wall, finally merging smoothly with the outer (inviscid) stream velocity U(x). At any point in the boundary layer, the fluid shear stress τ, is proportional to the local velocity gradient, assuming a Newtonian fluid. The value of the shear stress at the wall is most important, since it relates not only to the drag of the body but often also to its heat transfer. At the edge of the boundary layer, τ approaches zero asymptotically. There is no exact spot where τ=0, therefore the thickness δ of a boundary layer is usually defined arbitrarily as the point where u=0.99 U.